The paper is now greatly improved and in my opinion, as stated in the public discussion, ready for publication after a technical correction: the sentence in lines 10-11 of the new version is not true.
In fact, the extreme value theorem (Fisher-Tippett-Gnedenko theorem) states that in the case of independent AND IDENTICALLY DISTRIBUTED (not mentioned hypothesis) variables, IF the AM series converge, they can only converge to a GEV distribution - the theorem DOES NOT GRANT THE CONVERGENCE, i.e. the distribution may be not convergent! This aspect is very important in extreme value theory and cannot be neglected in the sentence. Moreover, the convergence to GP of the PoT series requires some additional hypotheses (that are not mentioned in the manuscript).
Given the introductory taste of the sentence, I think this comment can easily be addressed with a slight modification of the sentence to: "The extreme value theory showed that under some hypotheses - including independence - of the random variables, the AM and POT series can asymptotically converge only to the 3-parameters distributions known as GEV and GPD, respectively."
Best regards,
Francesco Marra |